List of practice Questions

If x + 1, 4x + 1, and 8x + 1 are in geometric progression, then what is the non-trivial value of x ?

If $x = 1 + a + a^2 + .................... $to infinity and $y = 1 + b + b^2 + ................... $to infinity, where a, b are proper fractions, then $1 + ab + a^2b^2 + .....$ to infinity is equal :

If $x^2 + 6x - 27 > 0$ and $x^2 - 3x - 4 < 0 $ then

If we add two vectors of equal magnitudes but in opposite directions, we get

If we plot volume of a certain mass of a gas against temperature at constant pressure, we get a straight line intersecting on the negative side at $ -273^{\circ}C$ which explains about absolute zero. This graph is known as

If work is done on a system, depends upon initial and final positions only it can be due to

If unit vectors $\hat{A}$ and $\hat{B}$ are inclined at an angle $\theta$, then $\left|\hat{A}-\hat{B}\right|$ is

If volume occupied by $CO_2$ molecules is negligible, then what will be the pressure $\left(\frac{p}{5.277}\right)$ exerted by one mole of $CO_{2}$ gas at $300\, K$? $\left(a = 3.592 atm L^{2} mol^{2}\right)$

If $ W_{1} $ be the work to be done to form a bubble of volume $ V $ from a given solution. The work required to be done to form a bubble of volume $ 2 V $ is

If $u = \sin (m \cos^{-1} x), v = \cos (m \sin^{-1} x)$, then $\frac{du}{dv} = $

If u represents object distance from pole of spherical mirror and $v$represents image distance from pole of mirror and f is the focal length of the mirror, then a straight line u = $v$ will,cut u versus $v$ graph at

If two numbers $p$ and $q $ are chosen randomly from the set $\{1, 2, 3, 4\}$ with replacement, then the probability that $ p^2 \ge 4q$ is equal to

If two squares are chosen at random on a chess board, the probability that they have a side in common is

If $U= \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$, $A = \{2, 4, 7\}$, $B = \{3, 5, 7, 9, 11\}$ and $C = \{7, 8, 9, 10, 11\}$, compute $(A \cap U) \cap (B \cup C)$.

If two circular arcs of the same length subtend angles of $60^{\circ}$ and $80^{\circ}$ at their respective centres, then the ratio of their radii is

If two coins are tossed 5 times, the chance that there will be 5 heads and 5 tails is

If two events are independent, then

If two identical bar magnets, each of length I , pole strength m and magnetic momen M are placed perpendicular to each other with their unlike poles in contact, the magnetic moment of the combination is

If $\theta =\cot^{-1}7+\cot ^{-1}8+\cot^{-1}18$, then $\cot\,\theta $ is equal to

If three particles of masses 2kg, 1kg and 3 kg are placed at comers of an equilateral triangle of perimeter 6m then the distance of center of mass which is at origin of particles from 1kg mass is (approximately) (Assume 2kg on x-axis )

If travelling at same speeds, which of the following matter waves have the shortest wavelength?

If $\theta$ and $\phi$ are acute angles, $\sin \, \theta = \frac{1}{2} , \cos \, \phi = \frac{1}{3},$ then the value of $\theta + \phi $ lies in

If $\theta$ and $\phi$ are the roots of the equation $8x^2 + 22x + 5 = 0$ , then

If the work done in stretching a wire by $1 \,mm$ is $2 J$, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by $1 \,mm$ is

If there were a smaller gravitational effect which of the following forces do you think would alter in some respect?